Exploring Mathematical Relationships Module 5: Investigation 2 Mathematically Similar Rectangles

Sequence of Squares Activity 5.2.1 Module 5: Investigation 2 Activity 5.2.1 – Sequence of Squares Activity 5.2.1 Sequence of Squares

Module 5: Investigation 2 Activity 5.2.1 – Sequence of Squares Open project 5-Altering Polygons - if online Save as a copy and add your name - if offline Save as and add your name Use the existing square block in a short script to draw a square of the side length of 20. Using the same script to draw squares with side lengths 40, 60, 80, 100… (if you do not clear the stage after drawing each square)

Module 5: Investigation 2 Activity 5.2.1 – Sequence of Squares Drag in the change side length by... block and keep it isolated. Explore it, use it. Explore the side length monitor in the stage. What is the difference between the blocks change side length by… and set side length to…?

Module 5: Investigation 2 Activity 5.2.1 – Sequence of Squares Clear the screen and build a script to draw the whole pattern of growing squares in one click. Have you used the repeat block to make your script short? How many squares are there in your pattern? What is the side length of the first square? The second square? What is the final side length drawn? What is the value of the side length variable at the end? Explain the difference.

Module 5: Investigation 2 Activity 5.2.1 – Sequence of Squares Discuss the scripts below, envisage the output of each script. What is the initial value of the side length variable in each script? What is its final value after finishing the repeat loop?

Module 5: Investigation 2 Activity 5.2.1 – Sequence of Squares Build a script to draw a row of identical squares next to each other. Build a script to draw a row of increasing squares, the first one having the side length of 20 and each one increasing by 10.

Module 5: Investigation 2 Activity 5.2.1 – [Extension] Sequence of Squares [Extension] Modify your previous script so the squares have a gap of 10 between them. [Extension] Modify your script so that each square has a random side length between 30 and 60.

Module 5: Investigation 2 Activity 5.2.1 – [Extension] Sequence of Squares [Extension] Here are three alternative solutions which all draw the output below. Discuss: which one is easier to read? ❸ ❶ ❷

Module 5: Investigation 2 Activity 5.2.1 – [Extension] Sequence of Squares [Extension] Try and recreate some of the patterns below by building on what you have done so far. Think of your own.

Altering Rectangles Activity 5.2.2 Module 5: Investigation 2 Activity 5.2.2 – Altering Rectangles Activity 5.2.2 Altering Rectangles

Continue in your 5-Altering Polygons project. Module 5: Investigation 2 Activity 5.2.2 – Altering Rectangles Continue in your 5-Altering Polygons project. Build a script to draw a rectangle with a height of 100 and base of 30. Make a new block called rectangle.

Module 5: Investigation 2 Activity 5.2.2 – Altering Rectangles Make a new variable called height and use it in the move block within the rectangle definition. Draw different rectangles by setting the value of height and running the block rectangle.

Module 5: Investigation 2 Activity 5.2.2 – Altering Rectangles Use the block change height by… inside repeat to draw various patterns of growing rectangles.

Module 5: Investigation 2 Activity 5.2.2 – Altering Rectangles Make a new variable called base and change your rectangle definition so that it uses both the variables height and base. Experiment with the Beetle pointing in different directions and drawing the same rectangle. What is the same and what is different about your rectangles?

Module 5: Investigation 2 Activity 5.2.2 – Altering Rectangles Read the scripts below and envisage the outcomes. Match the script with the set of rectangles it would create.

Module 5: Investigation 2 Activity 5.2.2 – Altering Rectangles Explore the line connecting the upper right corners of the rectangles. Some of them we call “magic”. What do you notice about the “magic” line? Are the first and last rectangles in each sequence the same?

Module 5: Investigation 2 Activity 5.2.2 – [Extension] Altering Rectangles [Extension] Try to create the patterns below or similar using your rectangle block:

Exploring Mathematical Similarity Module 5: Investigation 2 Activity 5.2.3 – Exploring Mathematical Similarity Activity 5.2.3 Exploring Mathematical Similarity

Continue in your project 5-Altering Polygons. Module 5: Investigation 2 Activity 5.2.3 – Exploring Mathematical Similarity Continue in your project 5-Altering Polygons. Build a script that sets the variables height to 60 and base to 30. Draw a rectangle using these values. Make the Beetle use the say… block to calculate and say the value of height divided by base. In the example above what does the number 2 represent?

Module 5: Investigation 2 Activity 5.2.3 – Exploring Mathematical Similarity Build another script which draws a rectangle, says… the value of height / base and then changes the values of height and base. Run the script several times and observe the sequence of rectangles and values.

Module 5: Investigation 2 Activity 5.2.3 – Exploring Mathematical Similarity Complete the tables A to D on your worksheet by doing the following steps: Build the two scripts. Click on the set blocks to set the height and base values. Click the second script and then note down the value displayed in the table – repeat this process seven more times. Ensure you have correctly set the height and base values before clicking on the second script.

Module 5: Investigation 2 Activity 5.2.3 – Exploring Mathematical Similarity

Module 5: Investigation 2 Activity 5.2.3 – Exploring Mathematical Similarity Complete the tables E to H on your worksheet by doing the following steps: Build the two scripts. Choose the initial values and the values to change … by … and type these into the empty holes (also note down on your worksheet). Click on the set blocks to set the height and base values. Click the second script and then note down the value displayed in the table – repeat this process seven more times. Can you build a script so that your sequence of rectangles has a “magic” line? Explain how you did this to another pupil. When there is a “magic” line what will the Beetle say?

Module 5: Investigation 2 Activity 5.2.3 – Exploring Mathematical Similarity

Unplugged: Rectangle Jumble Module 5: Investigation 2 Ext. Activity 5.2.4 – Unplugged: Rectangle Jumble Extension Activity 5.2.4 Unplugged: Rectangle Jumble

Module 5: Investigation 2 Ext. Activity 5.2.4 – Unplugged: Rectangle Jumble A school has a swimming pool that is 60 x 15 metres. Discuss which of these plans could be a scale drawing of the pool.

Module 5: Investigation 2 Ext. Activity 5.2.4 – Unplugged: Rectangle Jumble Sort these rectangles into three groups: rectangles with height 2 times the base (2 to 1) rectangles with height 3 times the base (3 to 1) rectangles with height 4 times the base (4 to 1)

Module 5: Investigation 2 Ext. Activity 5.2.4 – Unplugged: Rectangle Jumble For each of the scripts on the top row find a script on the bottom row that will draw a proportional rectangle.

Module 5: Investigation 2 My Investigation 2 check list: I built a script which draws a square using a variable for the side length. I built a script that draws a pattern of increasing squares using the change by block. I built a script to draw a rectangle using variables for the height and base. I built a script that draws a pattern of increasing rectangles using the change by block. I created a pattern of proportionally similar rectangles and explained the “magic” line. I envisaged which rectangles were proportionally similar to each other (from images as well as scripts).

Module 5 Investigation 2: Key Vocabulary a variables block which will change the current value of a variables by a specified amount.